Читать книгу Antenna and EM Modeling with MATLAB Antenna Toolbox - Sergey N. Makarov - Страница 24

Plot to scale the input impedance for a dipole antenna with l_A = 15 cm, a = 2 mm and over the band 200–1200 MHz using Eq. (1.14) and MATLAB.

Solution: First, we find the resonant frequency of an idealized dipole, which is f_res = c₀/(2l_A) = 3 × 10⁸/0.3 = 1 GHz. A simple MATLAB script given below uses Eq. (1.14) and outputs the plot shown in Figure 1.5 for the dipole impedance. One can see that the true resonance occurs at a bit lower frequency of 928 MHz; the resonant radiation resistance appears to be 60 Ω. According to Figure 1.2, this is still a very good match, which is close to the maximum radiated antenna power.

f = linspace(200e6, 1200e6, 1000);% Frequency, Hz lA = 0.15; % Dipole total length, m a = 0.002; % Dipole radius, m Za = dipoleAnalytical(f, lA, a); % Find resonant frequency Ra = real(Za); Xa = imag(Za); % Find resistance and reactance [dummy, index] = min(abs(Xa)); % Find resonant frequency fresMHz = f(index)/1e6 hold on; grid on; plot(f/1e6, Ra, 'b', 'LineWidth', 2); plot(f/1e6, Xa, 'r', 'LineWidth', 2); xlabel ('frequency, MHz'); ylabel ('Impedance, \Omega'); axis([min(f)/1e6 max(f)/1e6 -200 200]); title('Dipole resistance(blue) and reactance(red), \Omega'); line([fresMHz fresMHz],[-200 200]);

Figure 1.5 Dipole antenna impedance in the vicinity of its first (series) resonance. The dashed line shows the resonant frequency.

The MATLAB script above uses function dipoleAnalytical that corresponds to Eq. (1.14):

function [Za] = dipoleAnalytical(f, lA, a); % EM data epsilon = 8.85418782e-012; % Vacuum, F/m mu = 1.25663706e-006; % Vacuum, H/m c = 1/sqrt(epsilon*mu); % Vacuum, m/s eta = sqrt(mu/epsilon); % Vacuum, Ohm l = lA/2; % Dipole half length k = 2*pi*f/c; % Wavenumber z = k*l; % Electrical length corresponding to l R = -0.4787 + 7.3246*z + 0.3963*z.^2 + 15.6131*z.^3; X = -0.4456 + 17.0082*z - 8.6793*z.^2 + 9.6031*z.^3; Za = R - j*( 120*(log(l/a)-1)*cot(z)-X ); % Antenna impedance end